A student solved the following equation using the following steps:
2(2x+2)=4(x+4)
4x+4=4x+4
4=4
Conclusion: Infinitely many solutions
(2 points)
Based on the student's work, the equation was solved
The equation solved correctly would show that it has
solution(s).
Based on the student's work, the equation was NOT solved correctly. The correct solution of the equation should show that it has a single solution, not infinitely many solutions.
Based on the student's work, it appears that they made an error in their steps. Let's go through the solution and correct the mistake:
1. Start with the equation: 2(2x+2) = 4(x+4)
2. Apply the distributive property: 4x + 4 = 4x + 16
3. Subtract 4x from both sides of the equation: 4 = 16
4. Here is where the mistake occurred. The student ended up with the equation 4 = 16, which is false.
5. Since the equation is false, there are no solutions to the equation.
Conclusion: The statement that there are infinitely many solutions is incorrect. The correct conclusion is that there are no solutions to the equation.